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**MathBane** The question:

Under certain conditions, tsunami waves encountering land will develop into *bores*. A bore is a surge of water much like what would be expected if a dam failed suddenly and emptied a reservoir into a river bed. In the case of a bore traveling from the ocean into a dry river bed, one study shows that the velocity *V* of the tip of the bore is proportional to the square root of its height *h*. This is expressed in the formula below, where *k* is a constant.

$\displaystyle V = kh^{0.5}$

(a) A bore travels up a dry river bed. How does the velocity of the tip compare with its initial velocity when its height is reduced to one third of its initial height? (Round your answer to two decimal places.)

The velocity changes by a factor of [____].